<sect1 id="overview">
  <title>An Overview</title>
  <para>The data analysis tools package contains tools for
  statistical data analysis, random number generation and data
  sampling.  To use these tools, select the apropriate tool
  from the <guimenuitem>Statistical Analysis</guimenuitem>
  submenu of the <guimenu>Tools</guimenu> menu. The random number 
  generation tool is available from the <guimenuitem>Fill</guimenuitem>
  submenu of the <guimenu>Edit</guimenu> menu.
  The tools are described below.</para>

<figure id="analysistools">
    <title>Data Analysis Tools </title>
    <screenshot id="analysistools-shot">
	<graphic fileref="figures/analysistools-tools.png" format="PNG"></graphic>
    </screenshot>
</figure>

  <para>All tools have the same output options (see <xref linkend="outputoptions">).
  The results can
  be printed into a new sheet, into a new workbook, or into
  a given output range on a sheet of the current workbook.  To select the output method
  select one of the radio buttons inside the <guilabel>Output</guilabel>
  frame. If you have chosen <quote><guibutton>Output Range</guibutton></quote> you must also enter a single 
  range in the entry field.</para> 
  <para>Select the <guilabel>Autofit Columns</guilabel> option to automatically adjust the 
  widths of the columns in the output range.</para>
  <note><para>If the chosen output range is too
  small, some of the results will be lost.</para></note>
  <note><para>The
  old data in the output range is deleted and cannot be recovered.</para></note>

  <figure id="outputoptions">
      <title>Common output options of the data analysis tools</title>
      <screenshot id="outputoptions-shot">
	  <graphic fileref="figures/analysistools-outputoptions.png" format="PNG"></graphic>
      </screenshot>
  </figure>

  <para>To enter a range into an entry field, you can either type the 
  range specification into the text field, or click 
  in the text field and then select the range on the sheet (see 
  <xref linkend="specifyingranges">).</para>
  <figure id="specifyingranges">
    <title>Specifying Ranges</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ranges.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <para>Some entry fields accept lists of ranges. To enter these lists,
  select one range, type a comma, and then select the next range. At any 
  time, you may switch to another sheet of the workbook.</para>

</sect1>
<sect1 id="anova">
  <title>Analysis of Variance</title>

  <sect2 id="anova-single-factor-tool">
     <title>ANOVA: Single Factor Tool</title>

     <para>Use this tool to perform a single factor analysis of the
     variances of given variables. The variables are specified by the
     <quote><guilabel>Input Range:</guilabel></quote> entry.  The given range can be grouped 
     into the variables either
     by columns, by rows or by areas.  The <quote><guilabel>Alpha:</guilabel></quote> entry specifies the 
     significance level which is by default 5&#037;.</para>

     <para>If the first row or first column of the given range, or the 
     first field of each area contains labels, select the <quote><guibutton>Labels
     </guibutton></quote> option. The names of 
     the variables will be included in the  output table.</para>

     <para>The results of this analysis of variance are presented in 
     a standard ANOVA table. The <quote><guilabel>F critical</guilabel></quote>
     value is the largest value of F that is statistically significant
     using the given significance level (<quote><guilabel>Alpha</guilabel></quote>).</para>

     <para>This tool also calculates the count, sum, average,
     and the variance of each variable.</para>

   <figure id="anova-one-factor-tool-ex1">
    <title>1-factor ANOVA Dialog and Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ANOVA1-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
<example id="usinganovaonefactortool">
 <title>Using the single factor ANOVA</title>
     <para>See <xref linkend="anova-one-factor-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="anova-one-factor-tool-ex2">
     for the corresponding output.
     </para>
 </example>
  <figure id="anova-one-factor-tool-ex2">
    <title>Output From a 1-factor ANOVA</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ANOVA1-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     

  </sect2>

  <sect2 id="anova-two-factor-tool">
     <title>ANOVA: Two-Factor Tool</title>

     <para><application>Gnumeric</application> can perform two factor fixed effects ANOVAs with and 
     without replication. The same dialog is used and the 
     appropriate tool is selected depending on whether the number of rows 
     per sample is 1 or larger than 1.</para> 

  <sect3 id="anova-two-factor-without-tool">
     <title>ANOVA: Two-Factor Without Replication Tool</title>

     <para>If the number of rows per sample is given as 1, <application>Gnumeric</application> 
     performs a two factor fixed effects ANOVA without replication. Each
     column of the input range is interpreted as a level of the first 
     factor while each row is interpreted as a level of the second factor.
     </para>
     <para>The first row and column of the range may contain labels for 
     these levels. In this case the <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>
     <para> The <quote><guilabel>Alpha:</guilabel></quote> entry specifies the 
     significance level which is by default 5&#037;.</para>
 <example id="usinganovatwofactorwotool">
 <title>Using the 2-factor ANOVA Without Replication Tool</title>
     <para>See <xref linkend="anova-two-factor-without-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="anova-two-factor-without-tool-ex2">
     for the corresponding output.
     </para>
 </example>
  <figure id="anova-two-factor-without-tool-ex1">
    <title>2-factor ANOVA Without Replication Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ANOVA2wo-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="anova-two-factor-without-tool-ex2">
    <title>Output From a 2-factor ANOVA Without Replication</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ANOVA2wo-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect3>

  <sect3 id="anova-two-factor-with-tool">
     <title>ANOVA: Two-Factor With Replication Tool</title>
     <para>If the number of rows per sample is larger than 1, <application>Gnumeric</application> 
     performs a two factor fixed effects ANOVA with replication. Each
     column of the input range is interpreted as a level of the first 
     factor while groups of rows (the number of rows in each group given 
     by the <quote><guilabel>number of rows per sample</guilabel></quote> value) are interpreted as levels 
     of the second factor.
     </para>
     <para>The first row and column of the range may contain labels for 
     these levels. In this case the <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>
     <para> The <quote><guilabel>Alpha:</guilabel></quote> entry specifies the 
     significance level which is by default 5&#037;.</para>
     <para>See <xref linkend="anova-two-factor-with-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="anova-two-factor-with-tool-ex2">
     for the corresponding output.
     </para>
  <figure id="anova-two-factor-with-tool-ex1">
    <title>2-factor ANOVA With Replication Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ANOVA2w-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="anova-two-factor-with-tool-ex2">
    <title>Output From a 2-factor ANOVA With Replication</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ANOVA2w-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     
     <para><application>Gnumeric</application> will estimate missing values for each level combination as 
     the mean of the existing  values in that combination. The degrees of freedom 
     are adjusted appropriately. </para>

  </sect3>
  </sect2>

</sect1>

  <sect1 id="correlation-tool">
     <title>Correlation Tool</title>

  <figure id="correlation-tool-dialog">
    <title>Correlation Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-correlation.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>The correlation tool calculates the pairwise Pearson 
     correlation coefficients of the
     given variables.  Use this tool to calculate any number of
     correlation coefficients at the same time.  The variables for
     which the correlations are calculated are specified by the <quote><guilabel>Input
     Range:</guilabel></quote> entry. The input range can consist of either a single 
     range or a comma separated list of ranges. The given range or 
     ranges can be grouped by columns, by rows, or by areas.</para>

     <para>If the first row or column of the given ranges, or the 
     first field of each area contains labels,  the
     <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>

  <figure id="correlation-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-correlation-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>

 <example id="usingcorrelationtool">
 <title>Using the Correlation Tool</title>
    <para>For example, you want to calculate the correlation between
     three variables, one each in columns A, B, and C.
     Both variables have 10 values in rows 2 to 11 with labels in row 1
     (see <xref linkend="correlation-example-1">).</para>
<orderedlist>
     <listitem><para>
     Enter A1:B11 in the <quote><guilabel>Input Range:</guilabel></quote> entry by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting that range on the sheet. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Columns</guibutton></quote> radio button next to 
     <quote><guilabel>Grouped By:</guilabel></quote>, 
     since each variable is in its own column.</para></listitem>
     <listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
     option since the first row contains labels. (see 
     <xref linkend="correlation-example-2">).</para></listitem>
     <listitem><para> Specify the output 
     options as described above.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para>The calculated correlations are given in a table with each column and
     row labeled with the names of the variables.  If the
     names are not given in the input range, <application>Gnumeric</application> generates them.
     In our example, the 
     correlation between the variables in column A and B, can be found
     in the second column and third row of the results table (see 
     <xref linkend="correlation-example-3">).</para>
 </example>
  <figure id="correlation-example-2">
    <title>Completed Correlation Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-correlation-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="correlation-example-3">
    <title>Correlation Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-correlation-ex3.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect1>

  <sect1 id="covariance-tool">
     <title>Covariance Tool</title>

  <figure id="covariance-tool-dialog">
    <title>Covariance Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-covariance.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>The covariance tool calculates the pairwise 
     covariance coefficients of the
     given variables.  Use this tool to calculate any number of
     covariance coefficients at the same time.  The variables for
     which the covariances are calculated are specified by the <quote><guilabel>Input
     Range:</guilabel></quote> entry. The input range can consist of either a single 
     range or a comma separated list of ranges. The given range or 
     ranges can be grouped by columns, by rows, or by areas.</para>

     <para>If the first row or column of the given ranges, or the 
     first field of each area contains labels,  the
     <quote><guibutton>Labels</guibutton></quote> option should be selected.
     </para>

  <figure id="covariance-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-covariance-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>

 <example id="usingcovariancetool">
 <title>Using The Covariance Tool</title>
    <para>For example, you want to calculate the covariance between
     three variables, one each in columns A, B, and C.
     Both variables have 10 values in rows 2 to 11 with labels in row 1
     (see <xref linkend="covariance-example-1">).</para>
<orderedlist>
     <listitem><para>
     Enter A1:B11 in the <quote><guilabel>Input Range:</guilabel></quote> entry by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting that range on the sheet. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Columns</guibutton></quote> radio button next to 
     <quote><guilabel>Grouped By:</guilabel></quote>, 
     since each variable is in its own column.</para></listitem>
     <listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
     option since the first row contains labels.
     </para></listitem>
     <listitem><para> Specify the output 
     options as described above.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para>The calculated covariances are given in a table with each column and
     row labeled with the names of the variables.  If the
     names are not given in the input range, <application>Gnumeric</application> generates them.
     In our example, the 
     covariance between the variables in column A and B, can be found
     in the second column and third row of the results table (see 
     <xref linkend="covariance-example-2">).</para>
 </example>
  <figure id="covariance-example-2">
    <title>Covariance Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-covariance-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect1>


  <sect1 id="descriptive-statistics-tool">
     <title>Descriptive Statistics Tool</title>

  <figure id="descriptive-statistics-tool-dialog">
    <title>Descriptive Statistics Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-descstats.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>The descriptive statistics tool calculates various statistics 
     for the given variables and a confidence interval for the population
     mean. The variables are specified via the <quote><guilabel>Input
     Range:</guilabel></quote> entry.  The given range or list of ranges can be grouped into 
     variables by columns, rows, or areas.</para>

     <para>This tool can produce four different kinds of statistical
     data.
     </para>
     <itemizedlist>
     <listitem><para>If the <quote><guibutton>Summary Statistics</guibutton></quote> option is selected,  
     this tool calculates the
     mean, standard error, median, mode, standard deviation, sample
     variance, kurtosis, skewness, range, minimum, maximum, sum, and
     count for each variable.</para>
     </listitem>
     <listitem><para>If the <quote><guibutton>Confidence Interval for the Mean</guibutton></quote> option is 
     selected, the tool calculates  confidence intervals for the population
     mean of each variable.
     Specify the confidence level in the entry box.  The default confidence 
     level is 95&#037;.</para> 

     <note><para>The interval given will usually be wider than the 
     interval obtained using the CONFIDENCE function. The CONFIDENCE function
     assumes that the population standard deviation is known. This tool
     estimates the population standard deviation using the sample standard
     deviation.</para></note></listitem>

     <listitem><para>If the <quote><guibutton>Kth Largest:</guibutton></quote> option is selected, the tool finds
     the <parameter>k</parameter>th largest value of each of the variables.  Specify 
     <parameter>k</parameter> in
     the entry box next to the option. The default is 1.
     </para></listitem>

     <listitem><para>If the <quote><guibutton>Kth Smallest:</guibutton></quote> option is selected, the tool finds
     the <parameter>k</parameter>th smallest value of each of the variables.  Specify 
     <parameter>k</parameter> in
     the entry box next to the option. The default is 1.
     </para></listitem>
     </itemizedlist>
     <para>If the first entry for each variable contains the label,
     select the <quote><guibutton>Labels</guibutton></quote> option.
     </para>
  <figure id="descstats-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-descstats-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingdescstatstool"><title>Using the Descriptive Statistics Tool</title>
     <para><xref linkend="descstats-example-1"> shows some example data and 
     <xref linkend="descstats-example-2"> the corresponding output.
     </para>
</example>
  <figure id="descstats-example-2">
    <title>Descriptive Statistics Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-descstats-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect1>

  <sect1 id="forecasting-tools">
     <title>Forecast Tools</title>

  <sect2 id="exp-smoothing-tool">
     <title>Exponential Smoothing Tool</title>

  <figure id="smoothing-tool-dialog">
    <title>Exponential Smoothing Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-smoothing.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>The Exponential Smoothing tool performs the exponential
     smoothing for the given set or sets of values.  Each value in the
     smoothed set is predicted based on the forecast for the prior
     period.  The formula to calculate the forecast is: 
     <parameter>F(t+1) = F(t) + (1 - <guilabel>dampingFactor</guilabel>) 
     * (A(t) - F(t))</parameter>, 
     where <parameter>A(t)</parameter> is the <parameter>t</parameter>th
     value in the original data set.</para>

     <para>Specify the cells containing the datasets in the <quote><guilabel>Input
     Range</guilabel></quote> entry. The entered range or ranges are grouped into 
     datasets either by rows or by columns.</para> 

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

     <para>Specify prior forecast adjustment value in the
     <quote><guilabel>Damping factor</guilabel></quote> entry.  
     A value, for example, between 0.2 and 0.3 represents 20 to 30 percent error
     adjustment in the prior forecast.</para>

   <figure id="smoothing-example-1">
    <title>Some Example Data for the Exponential Smoothing Tool</title>
    <screenshot>
	<graphic fileref="figures/analysistools-smoothing-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingsmoothingtool"><title>Using the Exponential Smoothing Tool</title>
     <para><xref linkend="smoothing-example-1"> shows some example data and 
     <xref linkend="smoothing-example-2"> the corresponding output.
     </para>
</example>
  <figure id="smoothing-example-2">
    <title>Exponential Smoothing Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-smoothing-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect2>
  <sect2 id="moving-average-tool">
     <title>Moving Average Tool</title>

  <figure id="moving-tool-dialog">
    <title>Moving Average Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-moving-average.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>Use the moving average tool to calculate moving averages of
     one or more data sets.  A moving average provides useful trend information
     of the data that is lost in a simple average.  In addition,
     moving averages can be used to eliminate random variance.  For
     example, use this tool to create a smoother curve of a stock
     prize.</para>

     <para>Specify the cells containing the datasets in the <quote><guilabel>Input
     Range</guilabel></quote> entry. The entered range or ranges are grouped into 
     datasets either by rows or by columns.</para> 

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

     <para>Specify the <quote><guilabel>Interval</guilabel></quote> for the moving
     average.  The interval <parameter>i</parameter> is the number of consecutive values to be
     included in each moving average.</para>

     <para>The results are given in one column for each dataset  Each row represents the
     moving average of the corresponding row or column in the input range.  The
     moving average cannot be calculated for the first <parameter>k</parameter> rows in the
     input range where <parameter>k</parameter> is smaller than the given interval 
     <parameter>i</parameter>.</para>

   <figure id="moving-example-1">
    <title>Some Example Data for the Moving Average Tool</title>
    <screenshot>
	<graphic fileref="figures/analysistools-moving-average-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingmovingtool"><title>Using the Moving Average Tool</title>
     <para><xref linkend="moving-example-1"> shows some example data and 
     <xref linkend="moving-example-2"> the corresponding output.
     </para>
</example>
  <figure id="moving-example-2">
    <title>Moving Averages Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-moving-average-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect2>
  </sect1>

  <sect1 id="fourier-analysis-tool">
     <title>Fourier Analysis Tool</title>

  <figure id="fourier-tool-dialog">
    <title>Fourier Analysis Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-fourier.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>The Fourier Analysis tool normally performs a Fast Fourier Transform to obtain the 
     discrete fourier transform <parameter>F<subscript>s</subscript></parameter> of the given 
     sequence <parameter>f<subscript>t</subscript></parameter> of real numbers according to 
     the formula given in <xref linkend="fourier-tool-formula">.</para>
     <para>Select the <quote><guilabel>Inverse</guilabel></quote> option to calculate the
     inverse discrete fourier transform <parameter>f<subscript>t</subscript></parameter>
     of the given sequence <parameter>F<subscript>s</subscript></parameter> of real 
     numbers</para>
     <note><para>If the given sequences does not contain a number of terms that is a power 
     of 2 (i.e.
     2, 4, 8, 16, 32, 64, 128, etc.), this tool will append zeros to reach such a power of 
     2!</para></note>
     
     <para>Specify the cells containing the datasets in the <quote><guilabel>Input
     Range</guilabel></quote> entry. The entered range or ranges are grouped into 
     sequences either by rows or by columns.</para> 

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

  <figure id="fourier-tool-formula">
    <title>Fourier Analysis Formulae</title>
    <screenshot>
	<graphic fileref="figures/analysistools-fourier-formula.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <note><para>Before using the numbers obtained by this tool, ensure that these are in fact the 
     correct formulae for your discipline. In the physical sciences this fourier transform tends 
     to be called the inverse fourier transform and vice versa. Moreover, frequently the scaling 
     factor varies.</para>
     <para>For example <application>Mathematica</application> uses the terms fourier 
     transform and inverse fourier transform with the reversed meaning than 
     <application>Gnumeric</application> and it uses a scaling factor of 
     <parameter>1/SQRT(N)</parameter> rather than <parameter>1/N</parameter>.</para></note>
  </sect1>

  <sect1 id="ftest-two-sample-for-variances-tool">
     <title>F-Test: Two-Sample for Variances Tool</title>

  <figure id="ftest-tool-dialog">
    <title>F-Test Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ftest.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     <para>Use the F-Test tool to test whether two population  
     variances are different against the null hypothesis that
     they are not.</para>

     <para>Specify the variables in the <quote><guilabel>Variable 1 Range:</guilabel></quote>
     and <quote><guilabel>Variable 2 Range:</guilabel></quote> entries. The <quote><guilabel>Alpha:</guilabel></quote> 
     entry contains the 
     significance level which is by default 5&#037;.</para>

     <para>If the first field of each range contains labels, 
     select the <quote><guibutton>Labels</guibutton></quote> option. The names of 
     the variables will be included in the  output table.</para>

     <para>The results are given in a table.  This table contains
     the mean, variance, count of observations and the degree
     of freedom for both variables. The output table also includes the F-value,
     the one-tailed probability for the F-value, and the F Critical
     value for one-tailed test and the corresponding values for a two 
     tailed test. The one-tailed probability for the
     F-value (<quote><guilabel>P(F&lt;=f) one-tail</guilabel></quote> row) is the probability of making a
     Type I error in the one-tailed test. Similarly, the two-tailed 
     probability for the F-value (<quote><guilabel>P two-tail</guilabel></quote> row)
     is the probability of making a Type I error in the two-tailed test.
     Since in the two-tailed F-Test both critical values are positive, the
     <quote><guilabel>F Critical two-tail</guilabel></quote> row contains two numbers.</para>

     <para>If the output is directed into a specific output range, that
     range should contain at least three columns and eight rows.</para>

   <figure id="ftest-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ftest-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingftesttool"><title>Using the F-Test Tool</title>
     <para><xref linkend="ftest-example-1"> shows some example data and 
     <xref linkend="ftest-example-2"> the corresponding output.
     </para>
</example>
  <figure id="ftest-example-2">
    <title>F-Test Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-ftest-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
    
  </sect1>

  <sect1 id="histogram-tool">
     <title>Histogram Tool</title>

  <sect2 id="histogram-tool-intro">
     <title>Introduction</title>
     

  <figure id="histogram-tool-dialog">
    <title>Histogram Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-histogram.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>
     The histogram calculates several kinds of histograms for one or more 
     variables. The types of histogram created are determined by the options
     selected.  
     </para>

     <para>As shown in <xref linkend="histogram-tool-dialog">, the histogram dialog has four 
     tabs. We will introduce them in sequence.</para>
  </sect2>
  <sect2 id="histogram-tool-inputtab">
     <title>The <quote><guilabel>Input</guilabel></quote> Tab</title>
     <para>The <quote><guilabel>Input</guilabel></quote> tab contains the field specifying the 
     data to be used for the histogram.</para>
     <para>
     The <quote><guilabel>Input Range</guilabel></quote> entry contains a single range or a list of ranges, that
     can be grouped into variables by rows, columns, or areas. The <quote><guilabel>Bin Range</guilabel></quote>
     entry contains a single range of cutoff values. Both ranges may also include 
     labels.
     </para>
     <para>If the first row or column of the given input ranges, or the 
     first field of each area contains labels,  the
     <quote><guibutton>Input Labels</guibutton></quote> option should be selected.
     </para>

  </sect2>
  <sect2 id="histogram-tool-binstab">
     <title>The <quote><guilabel>Bins</guilabel></quote> Tab</title>
  <figure id="histogram-tool-dialog-bins">
    <title>Histogram Tool Dialog <quote><guilabel>Bins Tab</guilabel></quote></title>
    <screenshot>
	<graphic fileref="figures/analysistools-histogram-bins.png" format="PNG"></graphic>
    </screenshot>
  </figure>

  <para>The bins (or classes) for the histogram can either be predetermined by data 
  contained in your workbook or calculated by the histogram tool.</para>

  <para>Select the <quote><guilabel>Predetermined Bins</guilabel></quote> option to specify 
  data on your worksheet in the <quote><guilabel>Bin Range:</guilabel></quote> entry. The
  range should consist of a sigle column or two columns (the first one containing labels). If the 
  first column of the bin range contains labels, select the <quote><guibutton>Bin 
  Labels</guibutton></quote> option. The values in the last column are used as seprators between adjacent bins.</para> 

  <para>Select the <quote><guilabel>Calculated Bins</guilabel></quote> option to have the 
  bins determined by the tool. Enter the desired number of bins in the 
  <quote><guilabel>N:</guilabel></quote> entry. It is recommended (but optional) that you 
  specify the minimum and maximum cutoffs in the <quote><guilabel>Min:</guilabel></quote>
  and <quote><guilabel>Max:</guilabel></quote> entries.</para>
  </sect2>

  <sect2 id="histogram-tool-optionstab">
     <title>The <quote><guilabel>Options</guilabel></quote> Tab</title>

     <para> The options in the options tab modify the appearance of the histogram:</para>
     <itemizedlist>
     <listitem>
     <para> The <quote><guibutton>Pareto</guibutton></quote> option causes the bins to be 
     sorted by decreasing 
     frequency of the first variable.
     </para>
     </listitem>
     <listitem>
     <para> The <quote><guibutton>Percentages</guibutton></quote> option adds a histogram in terms 
     of 
     percentages rather than frequencies.
     </para>
     </listitem>
     <listitem>
     <para> The <quote><guibutton>Cumulative Percentages</guibutton></quote> option adds a 
     cumulative histogram.
     </para>
     </listitem>
     <listitem>
     <para> The <quote><guibutton>Chart</guibutton></quote> option is not implemented.
     </para>
     </listitem>
     </itemizedlist>

  </sect2>
  <sect2 id="histogram-tool-outputtab">
     <title>The <quote><guilabel>Output</guilabel></quote> Tab</title>
     <para>The Output tab contains the standard output options and fields 
     described in <xref linkend="overview">.</para>
  </sect2>
  <sect2 id="histogram-tool-example">
  <title>A Histogram Example</title>
  <figure id="histogram-example-1">
    <title>Some Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-histogram-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="histogram-example-3">
    <title>Specifying Bins</title>
    <screenshot>
	<graphic fileref="figures/analysistools-histogram-ex3.png" format="PNG"></graphic>
    </screenshot>
  </figure>

 <example id="usinghistogramtool">
 <title>Using the Histogram Tool</title>
    <para>For example, you want to calculate a histogram and a cumulative 
    histogram in percentages for a the number of successes in several 
    sequences of trials. The numbers of successes are recorded in column A 
    and the classes of interest in column D with labels in column C
     (see <xref linkend="histogram-example-1">).</para>
<orderedlist>
     <listitem><para>
     Enter A1:A21 in the <quote><guilabel>Input Range:</guilabel></quote> entry 
     of the <quote><guilabel>Input</guilabel></quote> tab by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting that range on the sheet. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Since you only have one variable select the <quote><guibutton>Areas</guibutton></quote> or 
     <quote><guibutton>Columns</guibutton></quote> radio 
     button next to <quote><guilabel>Grouped By:</guilabel></quote>.
     </para></listitem>
      <listitem><para> Select the <quote><guibutton>Input Labels</guibutton></quote>
     option since the first cell of the Input Range contains a label.</para></listitem> 
     <listitem><para>
     Enter C1:D5 in the <quote><guilabel>Bin Range:</guilabel></quote> entry
     of the <quote><guilabel>Bins</guilabel></quote> tab. The 
     <quote><guilabel>Predetermined Bins</guilabel></quote> option will now also be 
     selected (see <xref linkend="histogram-example-3">). </para></listitem>
      <listitem><para> Select the <quote><guibutton>Bin Labels</guibutton></quote>
     option since the first column of the Bin Range contains labels. 
     </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Percentage</guibutton></quote> and 
     <quote><guibutton>Cumulative Percentages</guibutton></quote> options
     of the <quote><guilabel>Options</guilabel></quote> tab.
     </para></listitem>     
     <listitem><para> In the <quote><guilabel>Output</guilabel></quote> tab, specify the output 
     options as described in <xref linkend="overview">.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para> The results are shown in 
     <xref linkend="histogram-example-2">.</para>
 </example>
  <figure id="histogram-example-2">
    <title>Histogram Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-histogram-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect2>
  </sect1>


  <sect1 id="random-number-generation-tool">
     <title>Random Number Generation Tool</title>

  <figure id="random-tool-dialog">
    <title>Random Number Generation Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-random.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>Use the random number generation tool to generate random
     numbers.  This tool can generate random numbers from various
     probability distributions.</para>

     <para>Specify the number of variables in
     the <quote><guilabel>Number of Variables:</guilabel></quote> entry.  This determines the
     number of columns of random values to be produced.</para>
     <para> Specify the number of random numbers for each variable in the 
     <quote><guilabel>Size of Sample:</guilabel></quote> entry.  This determines the number
     of rows of random values to be produced.</para>
     <para>  Specify the
     random distribution by selecting one of the items from the
     random distribution list.  The following random distributions are
     supported: Discrete, Normal, Poisson, Exponential, Binomial,
     Negative Binomial, Bernoulli, and Uniform.</para>
     <para>  Specify the parameters of the selected distribution:</para>

     <variablelist>
     <varlistentry><term>Discrete Random Distribution</term>
     <listitem>
        <para>Specify the value and
	probability input range in the <quote><guilabel>Value and Probability Input
	Range:</guilabel></quote> entry box.  The value and
	probability input range is a table consisting of two columns
	and any number of rows.  The first column specifies the
	discrete random values and the second column the probabilities
	for them.  The discrete random values do not have to be
	numbers, for example, strings will do as well.  The sum of the
	probabilities in the second column should be one.  For
	example, if you have the values A, B, C, and D in A1:A4 and
	values 0.1, 0.4, 0.2, and 0.3 in B1:B4, you would specify the
	value and probability input range to be A1:B4.</para>

	<note><para>If the probabilities do not add to 1, they will be 
	automatically scaled.</para></note>
     </listitem></varlistentry>

     <varlistentry><term>Normal Random Distribution</term>
     <listitem>
        <para>Specify the mean and the
	standard deviation.  The default values are 0 for the
	mean and 1 for the standard deviation.</para>
     </listitem></varlistentry>

     <varlistentry><term>Poisson Random Distribution</term>
     <listitem>
	<para>Specify the lambda in
	the <quote><guilabel>Lambda</guilabel></quote> entry. Lambda is the average 
	number of events in a unit time interval.</para>
     </listitem></varlistentry>

     <varlistentry><term>Exponential Random Distribution</term>
     <listitem>
	<para>Specify <parameter>b</parameter> in
	the <quote><guilabel>b Value</guilabel></quote> entry.</para>
     </listitem></varlistentry>

     <varlistentry><term>Binomial Random Distribution</term>
     <listitem>
	<para>Specify the
	probability of success (<parameter>p</parameter>) in the 
	<quote><guilabel>p Value</guilabel></quote> entry and  the
	number of trials (<parameter>n</parameter>) in the 
	<quote><guilabel>Number of Trials</guilabel></quote> entry.  
	The Binomial
	distribution is a discrete distribution in which the
	experiment consists of <parameter>n</parameter> identical trials. 
	Each trial is independent of other the trials
	and has two possible outcomes, a success or a failure.  The
	probability of success <parameter>p</parameter> is constant from 
	one trial to another.
	The mean of a random variable that has a Binomial distribution
	is <parameter>E(X) = np</parameter>, and the variance is 
	<parameter>var(X) = np(1-p)</parameter>.</para>
     </listitem></varlistentry>

     <varlistentry><term>Negative Binomial Distribution</term>
     <listitem>
	<para>Specify the
	probability of success <parameter>p</parameter> in the 
	<quote><guilabel>p Value</guilabel></quote> entry and the
	number of failures <parameter>r</parameter> in the 
	<quote><guilabel>Number of Failures</guilabel></quote> entry.
	Negative Binomial distribution is a discrete distribution in
	which the experiment consists of a sequence of independent
	trials.  Each trial has two possible outcomes, a success or a
	failure.  The probability of success <parameter>p</parameter> 
	is constant from one trial to another.  The experiment continues 
	until <parameter>r</parameter> failures
	are observed, where <parameter>r</parameter> is fixed in advance.  The mean of a
	random variable that has a Negative Binomial distribution is
	<parameter>E(X) = r(1-p)/p</parameter>, and the variance is <parameter>var(X) =
	r(1-p)/p^2</parameter>.</para>
     </listitem></varlistentry>

     <varlistentry><term>Bernoulli Random Distribution</term>
     <listitem>
        <para>Specify the probability of success (<parameter>p</parameter>) in the 
	<quote><guilabel>p Value</guilabel></quote> entry. <parameter>p</parameter>
	is a probability value between 0 and 1. The
        Bernoulli distribution has two random values 0 and 1, and
        <parameter>p</parameter> is the probability to observe value 1.  The mean of
        a random variable that has a Bernoulli distribution is <parameter>E(X) =
        1(p) + 0(1-p) = p</parameter>, and the variance is <parameter>var(X) = 
	p(1-p)</parameter>.</para>
     </listitem></varlistentry>

     <varlistentry><term>Uniform Random Distribution</term>
     <listitem>
        <para>Specify the range of
        the continuous random variable with the <quote><guilabel>Between:</guilabel></quote> 
	and <quote><guilabel>And:</guilabel></quote>
        entries.  The default values for these entries are 0 and 1.</para>
     </listitem></varlistentry>
     </variablelist>
   <figure id="random-example-1">
    <title>Some Example Data for the Random Number Generation Tool</title>
    <screenshot>
	<graphic fileref="figures/analysistools-random-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingrandomtool"><title>Using the Random Number Generation Tool</title>
     <para><xref linkend="random-example-1"> shows some example data and 
     <xref linkend="random-example-2"> the corresponding output.
     </para>
</example>
  <figure id="random-example-2">
    <title>Random Number Generation Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-random-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
   </sect1>

  <sect1 id="rank-and-percentile-tool">
     <title>Rank and Percentile Tool</title>

  <figure id="rank-and-percentile-tool-dialog">
    <title>Rank and Percentile Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-rank.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>Use this tool to rank given data and to calculate the
     percentiles of each data point.</para>
     <para>Specify the datasets to use in the <quote><guilabel>Input  
     Range:</guilabel></quote> entry.  
     The given range can be grouped into datasets by columns, by rows, or by areas.</para>

     <para>For each dataset, the tool creates three columns in the 
     output table:</para>
     <orderedlist>
     <listitem><para>The first column gives the indices of the 
     ordered data from largest to smallest data value.</para></listitem>
     <listitem><para>The second column 
     gives data values corresponding to the indices in the first column.</para></listitem>
     <listitem><para>The  third column indicates
     the percentile of the  data value in the second column.</para></listitem>
     </orderedlist>

     <para>If you have labels
     in the first cell of each data set, select the
     <quote><guilabel>Labels</guilabel></quote> option.</para>

   <figure id="rank-example-1">
    <title>Some Example Data for the Rank and Percentile Tool</title>
    <screenshot>
	<graphic fileref="figures/analysistools-rank-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingranktool"><title>Using the Rank and Percentile Tool</title>
     <para><xref linkend="rank-example-1"> shows some example data and 
     <xref linkend="rank-example-2"> the corresponding output.
     </para>
</example>
  <figure id="rank-example-2">
    <title>Rank and Percentile Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-rank-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <note><para>In the case of ties, the rank calculated by this tool differs from the 
  value of the RANK function for the same data. This tool calculates the rank as it is 
  normally used in Statistics: If two values are tied, the assigned rank is the average
  rank for those entries. For example in <xref linkend="rank-example-1"> the two values 10
  are the second and third largest values. Since they are equal each receives the rank of 
  2.5, the average of 2 and 3. The rank function on the other hand assigns the rank as it 
  is normally used to determine placements. The two values 10 would therefore each receive
  a rank of 2.   
  </para></note>
  </sect1>

  <sect1 id="regression-tool">
     <title>Regression Tool</title>
  <figure id="regression-tool-dialog">
    <title>Regression Tool Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-regression.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <para>The regression tool performs a multiple regression analysis.</para>
  <para>Enter a range or list of ranges containing the independent variables 
  into the <quote><guilabel>X Variables:</guilabel></quote> entry. These ranges 
  can be grouped into the various independent variables by columns, by rows, 
  or by areas. Select the appropriate option.</para>
  <para>Enter a single range containing the dependent variable into the
   <quote><guilabel>Y Variable:</guilabel></quote> entry.</para>
  <para>If the ranges for the independent and dependent variables also contains 
  labels in the first field of each row, column or area, select the <quote>
  <guilabel>Labels</guilabel></quote> option.</para>
  <para> Specify the confidence level in the <quote><guilabel>Confidence
  Level:</guilabel></quote> entry. The default is 95&#037;.</para>
  <para>To force the regression line or plane to pass through the origin, select the
  <quote><guilabel>Force Intercept To Be Zero</guilabel></quote> option.</para>
  <para>Specify the output options as described above. If the output is directed 
  into a specific output range, that
  range should contain at least seven columns and 17 rows more than there are 
  independent variables.</para>

  <figure id="regression-example-1">
    <title>Regression Example Data</title>
    <screenshot>
	<graphic fileref="figures/analysistools-regression-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>

 <example id="usingregressiontool">
 <title>Using the Regression Tool</title>
    <para>Suppose you want to perform a regression analysis on the data given in 
     <xref linkend="regression-example-1"> using <parameter>v</parameter> and 
     <parameter>y</parameter> as independent 
     variables and <parameter>u</parameter> as dependent variable.</para>
<orderedlist>
     <listitem><para>
     Enter B1:B9,E1:E9 in the <quote><guilabel>X Variables:</guilabel></quote> 
     entry by typing 
     this directly into the entry or clicking in the entry field and 
     then selecting the first part range on the sheet, typing comma, and then 
     selecting the second range. In the latter case the 
     entry will also contain the sheet name. </para></listitem>
     <listitem><para>
     Enter A1:A9  in the <quote><guilabel>Y Variable:</guilabel></quote> 
     entry. </para></listitem>
     <listitem><para>
     Select the <quote><guibutton>Columns</guibutton></quote> or 
     <quote><guibutton>Areas</guibutton></quote> option 
     since each variable is in its own column and also its own area.</para></listitem>
     <listitem><para> Select the <quote><guibutton>Labels</guibutton></quote>
     option since the first row contains labels. (see 
     <xref linkend="regression-example-2">).</para></listitem>
     <listitem><para> Specify the output 
     options as described above.</para></listitem>
     <listitem><para> Press the OK button. </para></listitem>
</orderedlist>
     <para> The output of this regression analysis is shown in
     <xref linkend="regression-example-3">.</para>
 </example>
  <figure id="regression-example-2">
    <title>Completed Regression Dialog</title>
    <screenshot>
	<graphic fileref="figures/analysistools-regression-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="regression-example-3">
    <title>Regression Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-regression-ex3.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect1>

  <sect1 id="sampling-tool">
     <title>Sampling Tool</title>
     <figure>
        <title>Sampling Tool Dialog</title>
	<screenshot>
	   	<graphic fileref="figures/analysistools-sampling.png" format="PNG"></graphic>
	</screenshot>
      </figure>
     <para>Use the sampling tool to take a sample of a data set.  This
     tool can take both a random sample of a given size or a periodic
     sample:</para>
     <variablelist>
     <varlistentry><term>random sample</term>
     <listitem><para>A random sample is a subset of the population such that 
     every subset of that size has the same chance of being picked.</para></listitem>
     </varlistentry>
     <varlistentry><term>periodic sample</term>
     <listitem><para>In a periodic sample every <parameter>k</parameter>th element in 
     the population is selected.</para></listitem>
     </varlistentry>
     </variablelist>

     <para>To use this tool, first specify the data set or data sets by setting the
     <quote><guilabel>Input Range:</guilabel></quote> entry. The range or ranges 
     given can be grouped into datasets by rows, by columns, or by areas.</para>
     <para>If the first entry in each data set contains a variable, select the 
     <quote><guilabel>Labels</guilabel></quote> option.</para>

     <para>Select the sampling method which
     can be either periodic or random.</para>
     <variablelist>
     <varlistentry><term>random sample</term>
     <listitem><para>Specify the size of the random sample in the <quote><guilabel>Size 
     of Sample:</guilabel></quote> entry.</para></listitem>
     </varlistentry>
     <varlistentry><term>periodic sample</term>
     <listitem><para>Specify the period in the <quote><guilabel>Period:</guilabel></quote>
     entry.</para></listitem>
     </varlistentry>
     </variablelist>

     <para>Specify the number of samples you would like to obtain in the <quote><guilabel>
     Number of Samples:</guilabel></quote> entry.</para>
     <note><para> Since the period uniquely determines a periodic sample, if you specify 
     that you would like 2 samples you will be given the identical sample twice.</para></note>
     <note><para>If the dataset for a periodic sample is a two dimensional range, <application>Gnumeric</application> 
     will enumerate the data points by row first.</para></note>

   <figure id="sampling-example-1">
    <title>Some Example Data for the Sampling Tool</title>
    <screenshot>
	<graphic fileref="figures/analysistools-sampling-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
 <example id="usingsamplingtool"><title>Using the Sampling Tool</title>
     <para><xref linkend="sampling-example-1"> shows some example data and 
     <xref linkend="sampling-example-2"> the corresponding output.
     </para>
</example>
  <figure id="sampling-example-2">
    <title>Sampling Tool Output</title>
    <screenshot>
	<graphic fileref="figures/analysistools-sampling-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect1>


<sect1 id="t-test">
     <title>Comparing Means of 2 Populations</title>
     <para><application>Gnumeric</application> provides 4 similar tools to test whether the difference 
     of two population means is equal to a hypothesized value. These 
     four tools use the same dialog (see <xref linkend="ttest-dialog">).</para>

  <figure id="ttest-dialog">
    <title><parameter>t</parameter>- and <parameter>z</parameter>-Test Tool Dialog</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest.png" format="PNG"></graphic>
    </screenshot>
  </figure>

     <para>Depending on the options settings, the appropriate test will be performed. The 
     entries in the <quote><guilabel>Input</guilabel></quote>, <quote><guilabel>Test</guilabel></quote>, and 
     <quote><guilabel>Output</guilabel></quote> frames are independent from the specific test.</para>

     <para>Enter the first variable in the <quote><guilabel>Variable 1 Range</guilabel></quote> entry 
     and the second variable in the <quote><guilabel>Variable 2 Range</guilabel></quote> entry.</para>
     <para>Enter the hypothesized difference between the population means in the 
     <quote><guilabel>Hypothesized Mean Difference</guilabel></quote> entry, which has a default of 0.
     Enter the significance level in the <quote><guilabel>Alpha</guilabel></quote> entry, which has a 
     default of 5 &#037;.</para>
     <para> Specify the output 
     options as described above. If the output is printed into a range, it should have at
     least three columns and ten rows.</para>

     <para>There are up to three possible options that can be selected:</para>
     <variablelist>
     <varlistentry><term><quote><guilabel>Paired</guilabel></quote> versus <quote><guilabel>Unpaired</guilabel></quote>
     </term><listitem><para>
     If the variables are dependent (or paired) select the <quote><guilabel>Paired</guilabel></quote>
     option.
     </para></listitem>
     </varlistentry>
     <varlistentry><term><quote><guilabel>Known</guilabel></quote> versus <quote><guilabel>Unknown</guilabel></quote>
     </term><listitem><para>
     For unpaired or independent variables, the population variances may be known 
     or unknown. In the latter case they will be estimated using the sample variances.
     Select the <quote><guilabel>Known</guilabel></quote> option if you in fact know the population 
     variances prior to collecting the sample.
     </para></listitem>
     </varlistentry>
     <varlistentry><term><quote><guilabel>Equal</guilabel></quote> versus <quote><guilabel>Unequal</guilabel></quote>
     </term><listitem><para>
     For paired variables with unknown population variances, we may either assume 
     that the population variances are equal or not. If the population variances are
     assumed to be equal, <application>Gnumeric</application> will estimate the common variance by pooling the 
     sample variances. Select the <quote><guilabel>Equal</guilabel></quote> option to assume that
     the population variances are equal.
     </para></listitem>
     </varlistentry>
     </variablelist>

  <sect2 id="t-test-paired-two-samples-for-means-tool">
     <title><parameter>t</parameter>-Test: Paired Two Sample for Means Tool</title>
  <figure id="ttest-dialog-paired">
    <title><parameter>t</parameter>-Test (Paired) Tool Dialog Options</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-paired.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     <para>For paired variables, when you click on 
     <quote><guibutton>OK</guibutton></quote>, <application>Gnumeric</application> will test whether the 
     mean of the difference between the paired variables is equal to 
     the given hypothesized mean difference.</para>

 <example id="usingttestpairedtool">
 <title>Using the <parameter>t</parameter>-Test (Paired) Tool</title>
     <para>See <xref linkend="ttest-paired-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="ttest-paired-tool-ex2">
     for the corresponding output.
     </para>
 </example>
  <figure id="ttest-paired-tool-ex1">
    <title><parameter>t</parameter>-Test (Paired) Example Data</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-paired-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="ttest-paired-tool-ex2">
    <title>Output from the <parameter>t</parameter>-Test (Paired) Tool</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-paired-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>

  </sect2>

  <sect2 id="t-test-two-sample-equal-variances-tool">
     <title><parameter>t</parameter>-Test: Two-Sample Assuming Equal Variances Tool</title>
  <figure id="ttest-dialog-equal">
    <title><parameter>t</parameter>-Test (Equal Variances) Tool Dialog Options</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-equal.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     <para>For unpaired variables with unknown but assumed equal population variances,
     when you click on <quote><guibutton>OK</guibutton></quote>, <application>Gnumeric</application> will test whether the 
     mean of the difference between the paired variables is equal to the given hypothesized
     mean difference.</para>

 <example id="usingttestequaltool">
 <title>Using the <parameter>t</parameter>-Test (Unknown but Equal Variances) Tool</title>
     <para>See <xref linkend="ttest-equal-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="ttest-equal-tool-ex2">
     for the corresponding output.
     </para>
 </example>
  <figure id="ttest-equal-tool-ex1">
    <title><parameter>t</parameter>-Test (Unknown but Equal Variances) Example Data</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-equal-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="ttest-equal-tool-ex2">
    <title>Output from the <parameter>t</parameter>-Test (Unknown but Equal Variances) Tool</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-equal-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect2>

  <sect2 id="t-test-two-samples-unequal-variances">
     <title><parameter>t</parameter>-Test: Two-Sample Assuming Unequal Variances Tool</title>
  <figure id="ttest-dialog-unequal">
    <title><parameter>t</parameter>-Test (Unknown and Unequal Variances) Tool 
    Dialog Options</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-unequal.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     <para>For unpaired  variables with unknown and assumed unequal population variances,
     when you click on <quote><guibutton>OK</guibutton></quote>, <application>Gnumeric</application> will test whether the 
     mean of the difference between the paired variables is equal to the given hypothesized
     mean difference.</para> 

 <example id="usingttestunwqualtool">
 <title>Using the <parameter>t</parameter>-Test (Unknown and Unequal Variances) Tool</title>
     <para>See <xref linkend="ttest-unequal-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="ttest-unequal-tool-ex2">
     for the corresponding output.
     </para>
 </example>
  <figure id="ttest-unequal-tool-ex1">
    <title><parameter>t</parameter>-Test (Unknown and Unequal Variances) Example Data</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-unequal-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="ttest-unequal-tool-ex2">
    <title>Output from the <parameter>t</parameter>-Test (Unknown and Unequal Variances) 
    Tool</title>
    <screenshot>
<graphic fileref="figures/analysistools-ttest-unequal-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect2>

  <sect2 id="ztest-two-samples-for-means-tool">
     <title<parameter>z</parameter>-Test: Two Samples for Means Tool</title>
  <figure id="ztest-dialog">
    <title><parameter>z</parameter>-Test Tool Dialog Options</title>
    <screenshot>
<graphic fileref="figures/analysistools-ztest.png" format="PNG"></graphic>
    </screenshot>
  </figure>
     <para>For unpaired  variables with known population variances, enter those variances 
     in the <quote><guilabel>Variable 1 Pop. Variance</guilabel></quote> and 
     <quote><guilabel>Variable 2 Pop. Variance</guilabel></quote> entries.
     When you click on <quote><guibutton>OK</guibutton></quote>, <application>Gnumeric</application> will test whether the 
     mean of the difference between the paired variables is equal to the given hypothesized
     mean difference.</para> 

 <example id="usingztesttool">
 <title>Using the <parameter>z</parameter>-Test Tool</title>
     <para>See <xref linkend="ztest-tool-ex1"> for an example 
     of a completed dialog and <xref linkend="ztest-tool-ex2">
     for the corresponding output.
     </para>
 </example>
  <figure id="ztest-tool-ex1">
    <title><parameter>z</parameter>-Test Example Data</title>
    <screenshot>
<graphic fileref="figures/analysistools-ztest-ex1.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  <figure id="ztest-tool-ex2">
    <title>Output from the <parameter>z</parameter>-Test Tool</title>
    <screenshot>
<graphic fileref="figures/analysistools-ztest-ex2.png" format="PNG"></graphic>
    </screenshot>
  </figure>
  </sect2>
</sect1>

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